Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim |Rn(x)=0 f(x)=ex f(x) = e a=0 n-∞ First find a formula for f (n) (x). f(n) (x) = (Type an exact answer.) Next, write the formula for the remainder. n+1 Rn(x) = (n+1)! for some value c between x and 0 = 0 for all x in the interval of convergence. (Type exact answers.) Find a bound for Rn(x) that does not depend on c, and thus holds for all n. Choose the correct answer below. ex elx OC. R(x)(n+1 OE. Rn(x)(n+1) | Rn (x)| = (n+1)* = 0 for all x in the interval of convergence by taking the limit of the bound from above and using limit rules. Choose the correct reasoning below. Show that lim R,(x)=0 OA. Use the fact that lim U = 0 for all x to obtain lim |R,(x)| = el*1.0=0. OB. Use the fact that lim = 0 for all x to obtain lim |R,(x)=1+0=0. OC. Use the fact that lim A(+1) (n+1)! = 0 for all x to obtain lim R₁(x) =+0=0. e OD. Use the fact that lim = 0 for all x to obtain fim R₁(x)| =…

Consider the following parametric equations, x=-4t, y=-7t+ 13; -10 sts 10. Complete parts (a) through (d) below. a. Make a brief table of values of t, x, and y t x(t) y(t) 10 -6 0 6 10 (Type integers or decimals.) ○ A. b. Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing t). 130 G c. Eliminate the parameter to obtain an equation in x and y. d. Describe the curve. OA. A line segment falls from left to right as t increases OB. A line segment falls from right to left as t increases OC. A line segment rises from right to left as t increases OD. A line segment rises from left to right as t increases

Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. -1 y=10 (1+10x) 1 y= 0, x = 0, and x=2 Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice and fill in the answer boxes to complete your choice. (Type exact answers.) OA. S dx O B. dy The volume is (Type an exact answer.)